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Points B and C lie on AD. The length of AB is 4 times the length of BD

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Points B and C lie on AD. The length of AB is 4 times the length of BD  [#permalink]

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New post 27 Mar 2019, 21:00
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (02:06) correct 21% (02:54) wrong based on 14 sessions

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Joined: 27 Sep 2018
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Re: Points B and C lie on AD. The length of AB is 4 times the length of BD  [#permalink]

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New post 27 Mar 2019, 22:08
AB=4BD
AD-BD=4BD
AD=5BD. (I)

Also AC=9CD
AD-CD=9CD
AD=10CD. (II)
MULTIPLYING (I) BY 2 AND SUBTRACTING BY (II)
AD=10(BD-CD)=10BC
BC/AD=1/10

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Re: Points B and C lie on AD. The length of AB is 4 times the length of BD  [#permalink]

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New post 27 Mar 2019, 22:34
AB = 4BD = 4(BC+BD) = 4BC + 4CD.

=> AB = 4BC + 4CD
Adding BC to both sides of the equality, AB + BC = 5BC + 4CD
=> AC = 5BC + 4CD

We already know, AC = 9CD. Therefore, 9CD = 5BC + 4CD => 5CD = 5BC => CD = BC.
Hence, AC = 9BC.

Again, AD = AC + CD => AD = 9BC + BC => AD = 10BC
Therefore, BC = (1/10)AD

Ans. option C.
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Re: Points B and C lie on AD. The length of AB is 4 times the length of BD  [#permalink]

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New post 27 Mar 2019, 23:11
Bunuel wrote:
Points B and C lie on AD. The length of AB is 4 times the length of BD, and the length of AC is 9 times the length of CD. The length of BC is what fraction of the length of AD ?

(A) 1/36
(B) 1/13
(C) 1/10
(D) 5/36
(E) 1/5



Say AD is 10 units.

A-------------------------------------------------D


A----------------------------------B--------------D
AB = 8, BD = 2 (Ratio of 4:1)

A-------------------------------------------C-----D
AC = 9, CD = 1 (Ratio of 9:1)

BC = AC - AB = 9 - 8 = 1

BC/AD = 1/10

Answer (C)
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Re: Points B and C lie on AD. The length of AB is 4 times the length of BD   [#permalink] 27 Mar 2019, 23:11
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Points B and C lie on AD. The length of AB is 4 times the length of BD

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